In a curve interpolation in association with a numerical control apparatus, interpolation of an involute curve has particularly been needed for machining gears, vanes of pumps and the like, and it has been a general practice to interpolate the involute curve with a computer or an NC program producing system which are distinctly provide from the numerical control apparatus to analyze a curve data into straight line data, whereupon numerical control machinings are performed with the use of a tape.
The same applicant filed a Japanese patent application No. 62-157303 on June 24, 1987 entitled "INVOLUTE INTERPOLATION METHOD" in which it is proposed to readily interpolate an involute curve in a numerical control apparatus.
According to the involute interpolation method proposed therein, coordinates of an arbitrary point on the involute curve are defined by the following equations: EQU X=R{cos (.theta.+.theta.1)+.theta. sin (.theta.+.theta.1)}+X.sub.O EQU [Y=R{sin (.theta.+.theta.1)-.theta. cos (.theta.+.theta.1)}+Y.sub.O
The angle is incremented at every predetermined value from .theta.=(.theta.2-.theta.1) to .theta.=(.theta.3-.theta.1) to sequentially plot points on the involute curve and then compute moving distances between adjacent two points, whereupon a straight line interpolation at a specified speed is performed.
However, since the increment of the angle .theta. is set at constant, a rotational radius of the involute curve increases attendant to the increment of the angle, thereby causing to increase the speed, and thus a problem is introduced in that a cutting speed is not maintained at constant.